Question

Drawing a card- four cards are drawn from a desk without replacement.Find these probabilities.

Answer 1

The deck consists of 4 jacks, 26 black cards, and 13 hearts.

There is only 1 way of drawing all 4 jacks: $\dbinom44=\dfrac{4!}{4!(4-4)!}=1$.

There are $\dbinom{26}4=14,950$ ways of drawing 4 black cards.

There are $\dbinom{13}4=715$ ways of drawing 4 hearts.

There are $\dbinom{52}4=270,725$ ways of drawing any 4 cards.

The probabilities are then

a.

$\dfrac{\binom44}{\binom{52}4}=\dfrac1{207,725}\approx0.00000369$

b.

$\dfrac{\binom{26}4}{\binom{52}4}=\dfrac{46}{833}\approx0.0552$

c.

$\dfrac{\binom{13}4}{\binom{52}4}=\dfrac{11}{4165}\approx0.00264$